By Jerzy Neyman (1956)
(1) FISHER’S allegation that, contrary to some passages in the introduction and on the cover of the book by Wald, this book does not really deal with experimental design is unfounded. In actual fact, the book is permeated with problems of experimentation. (2) Without consideration of hypotheses alternative to the one under test and without the study of probabilities of the two kinds, no purely probabilistic theory of tests is possible. (3) The conceptual fallacy of the notion of fiducial distribution rests upon the lack of recognition that valid probability statements about random variables usually cease to be valid if the random variables are replaced by their particular values. The notorious multitude of “paradoxes” of fiducial theory is a consequence of this oversight. (4) The idea of a “cost function for faulty judgments” appears to be due to Laplace, followed by Gauss.
In a recent article (Fisher, 1955), Sir Ronald Fisher delivered an attack on a a substantial part of the research workers in mathematical statistics. My name is mentioned more frequently than any other and is accompanied by the more expressive invectives. Of the scientific questions raised by Fisher many were sufficiently discussed before (Neyman and Pearson, 1933; Neyman, 1937; Neyman, 1952). In the present note only the following points will be considered: (i) Fisher’s attack on the concept of errors of the second kind; (ii) Fisher’s reference to my objections to fiducial probability; (iii) Fisher’s reference to the origin of the concept of loss function and, before all, (iv) Fisher’s attack on Abraham Wald.
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See also: Neyman’s Nursery: OCTOBER 22
Some of you may have read my “Neyman’s Nursery” posts. Well, an additional one that I wrote but never posted was to be called something like “Twilight Zone in Neyman’s Nursery”*. In the “Nursery” posts I mentioned discovering Neyman’s use of power post-data in the “hidden Neyman” papers (maybe 8 years ago), and how at odds those papers were from the more typical pre-data power idea (wherein power arises only in the planning). When I came back to this 1956 paper, which I’d read several times before, I was shocked to find him noting the third use of power, post-data. But this issue about the use of power post-data is a major, major one in the foundations of statistics—or so I hold.
*I didn’t think others would really get it.
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